Two ways of setting a post with a concrete foundation exist. The most common way is to surround the bottom of the post in concrete, which is typically called pouring a post footing. A standalone pier is a poured concrete form that a post is set on top of. One of the advantages of this method of installation is that concrete typically outlasts even the best-treated lumber fence posts. This allows for a footing that can have a new post attached to its top in line with the existing fence.
Remove the fasteners holding the fence to the post. These may be screws or nails driven directly into the face of the post or screws or bolts fastened to brackets. Use a drill, impact gun or wrench to loosen bolts and screws. Use a large pry bar for nailed joints.
Drive a wooden stake into the ground near the post, setting the detached fence panel against it for bracing. Be sure to shift the panel over sufficiently to create good access to the damaged post.
Assess the attachment of the post. It will be attached to the pier with a metal bracket mounted with either bolts stuck into the concrete with nuts threaded down to anchor them or with concrete screws or masonry lag bolts and anchor shields in the concrete.
Remove the screws or bolts on the side of the bracket that hold the post in the bracket and set it aside. Examine the bracket for signs of rust or other deterioration or damage. Reuse an undamaged bracket that is securely mounted. Remove the lags or screws from a damaged bracket using a cordless drill or impact gun.
Set a new bracket, if needed, of the same size as the end of your post. Align it with the fence. Surface mounting brackets for 4-by-4-inch and round metal posts are available from most fence retailers. Mark the screw holes through the base of the bracket onto the concrete of the pier. Drill a pilot hole in each marked location with a 3/16-inch rotary mason's bit to a depth of 2 ½ inches. Blow the dust from the hole.
Position the bracket and install a tapcon-style concrete screw ¼-by-2 ¼-inch into each pilot hole. Tighten the screws firmly.
Cut the new post to the same height as the original. Use a reciprocating saw for either wood, vinyl or metal posts. Set the post into the bracket and install fasteners through the edges of the bracket into the sides of the post. Use 1 ¼-inch treated deck screws for wood or 1-inch self tapping sheet metal screws for metal or vinyl posts. Use one screw for each hole.
Reattach the fence panels to the new post in the same way they were attached to the original.